Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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16 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   8 Unit Circle Trigonometry/
  4.    wt: 6:   6 Trigonometry first steps/
  5.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  6.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  7.    wt: 5:   12 Function Translating and Rescaling/
  8.    wt: 5:   11 Parallel Straight Lines and Transversals/
  9.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  10.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  11.    wt: 5:   7 Complex Numbers/
  12.    wt: 5:   5 What is Similarity/
  13.    wt: 5:   4 Lines and Slopes Take 1/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/

Web Page Search

56 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   13 Addition and Addition Tables
  3.    wt: 2:   4 Angles on Maps Plans drawn to scale
  4.    wt: 2:   3 Lengths and Areas on Maps and Plans
  5.    wt: 2:   11 Signed Number Addition and Addition Properties
  6.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  7.    wt: 1:   About site lesson plans
  8.    wt: 1:   3 Polynomials Multiplication Addition
  9.    wt: 1:   13 Velocity Vectors in Physics
  10.    wt: 1:   10 Parallelogram Addition Method
  11.    wt: 1:   8 Parallel Vectors
  12.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  13.    wt: 1:   6 Vectors with Coordinates
  14.    wt: 1:   5 Head To Tail Arrow Addition
  15.    wt: 1:   3 Navigation with Arrows or Vectors
  16.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  17.    wt: 1:   1 Unit Points Reflections Rotations
  18.    wt: 1:   Unit Circle Development of Trigonometry
  19.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  20.    wt: 1:   8 Unit Circle Development of Trigonometry
  21.    wt: 1:   3 Addition Properties
  22.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  23.    wt: 1:   Why Trigonometry the whyslopes view
  24.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  25.    wt: 1:   8 Distance Between Points on a Line
  26.    wt: 1:   5 Cartesian Addition and Translation
  27.    wt: 1:   PS G Rotation Distributes over Addition
  28.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  29.    wt: 1:   PS D Addition with Cartesian Coordinates
  30.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  31.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  32.    wt: 1:   6 Figuring with Maps Not to Scale
  33.    wt: 1:   21 Addition of Multiples of a Single Vector
  34.    wt: 1:   19 Signed Multiples of Vectors
  35.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  36.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  37.    wt: 1:   15 Head to Tails in place Addition Associative
  38.    wt: 1:   13 Arrows and Vectors in a Plane
  39.    wt: 1:   4 Location of Point in Decimal Addition
  40.    wt: 1:   A Decimal Addition Columm Methods
  41.    wt: 1:   2 Combing Counts Addition Skills and Principles
  42.    wt: 1:   2 Addition and Multiplication Axioms
  43.    wt: 1:   11 Real Number Addition
  44.    wt: 1:   8 Coordinates for Maps and Planes
  45.    wt: 1:   3 GE III Equation Addition and Multiplication
  46.    wt: 1:   3 signed coordinates for maps and planes
  47.    wt: 1:   1 Addition and Subtraction with Units
  48.    wt: 1:   16 Addition Subtraction Comparision Compared
  49.    wt: 1:   1. Explaining Addition Table
  50.    wt: 1:   010 Repeated Addition of Time Intervals
  51.    wt: 1:   8 Addition of Time Intervals via subtotaling
  52.    wt: 1:   7 Addition of Time Intervals
  53.    wt: 1:   Chapter 23 Links To Trigonometry
  54.    wt: 1:   Chapter 21 Arrow Addition
  55.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  56.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

261 matches:

  1.    wt: 9:   4 Angles on Maps Plans drawn to scale
  2.    wt: 9:   3 Lengths and Areas on Maps and Plans
  3.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  4.    wt: 8:   6 Figuring with Maps Not to Scale
  5.    wt: 7:   13 Velocity Vectors in Physics
  6.    wt: 7:   10 Parallelogram Addition Method
  7.    wt: 7:   8 Parallel Vectors
  8.    wt: 7:   7 Coordinate Addition and Scalar Multiplication
  9.    wt: 7:   6 Vectors with Coordinates
  10.    wt: 7:   5 Head To Tail Arrow Addition
  11.    wt: 7:   3 Navigation with Arrows or Vectors
  12.    wt: 7:   1 Unit Points Reflections Rotations
  13.    wt: 7:   Unit Circle Development of Trigonometry
  14.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  15.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  16.    wt: 7:   Why Trigonometry the whyslopes view
  17.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  18.    wt: 7:   A Measurement with Ruler Proper Use
  19.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  20.    wt: 7:   2 Measuring Area Directly
  21.    wt: 7:   1 Length Measurement
  22.    wt: 6:   A Global Time and Navigation
  23.    wt: 6:   15 Dot and Cross Product
  24.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  25.    wt: 6:   12 From Applied To Pure Mathematics
  26.    wt: 6:   11 Component Method
  27.    wt: 6:   9 Head to Tail Coordinate View
  28.    wt: 6:   4 Resultant of a Sum of Movements
  29.    wt: 6:   2 Signed Coordinates
  30.    wt: 6:   1 Unsigned Coordinates
  31.    wt: 6:   Vector and Complex Number Applet
  32.    wt: 6:   13 Straight Lines Finding Equations from 2 points
  33.    wt: 6:   17 tangent function angle sum formulas
  34.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  35.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  36.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  37.    wt: 6:   32 seven rows of pascals triangle
  38.    wt: 6:   31 basic secant cosecant cotangent trig identities
  39.    wt: 6:   30 unit circle calculation of six trigonometric functions
  40.    wt: 6:   29 secant cosecant and cotangent for acute angles
  41.    wt: 6:   28 Expressing products of sines cosines as sums
  42.    wt: 6:   27 Logarithmic use of products of sines and cosines
  43.    wt: 6:   26 Formulas for products of sines and cosines
  44.    wt: 6:   25 tangent double angle formula Slope connection
  45.    wt: 6:   24 tangent Angle Difference Formula
  46.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  47.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  48.    wt: 6:   21 sine and cosine Half Angle Formulas
  49.    wt: 6:   20 sine and cosine Double Angle Formulas
  50.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  51.    wt: 6:   18 sum of sinusoidal waves as a single wave
  52.    wt: 6:   17G Pythagorean Theorem Converse
  53.    wt: 6:   17F Law of cosines
  54.    wt: 6:   17E Trig Formulas for dot and cross Products
  55.    wt: 6:   17D cis formulas for sine cosines and tangent
  56.    wt: 6:   17C sine and cosine double triple angle formulas
  57.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  58.    wt: 6:   17A The complex number valued trig function cis
  59.    wt: 6:   16 Right Triangle Complementary Angle Relations
  60.    wt: 6:   15 sine cosine Complementary Angle Relations
  61.    wt: 6:   14 cosine even and sine and tangent are odd
  62.    wt: 6:   13 Graph of tangent function many periods
  63.    wt: 6:   12 Graph of tangent function for one period
  64.    wt: 6:   11 tangent function undefined when terminal side vertical
  65.    wt: 6:   10 Graphs of sines and cosines many periods
  66.    wt: 6:   9 Graphs of sine and cosine over one period
  67.    wt: 6:   8 period of tangent function
  68.    wt: 6:   7 period of sine and cosine
  69.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  70.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  71.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  72.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  73.    wt: 6:   2 Quadrant I reference Angles
  74.    wt: 6:   8 Unit Circle Development of Trigonometry
  75.    wt: 6:   3 Addition Properties
  76.    wt: 6:   8 Triangles Cascade Problem Solving
  77.    wt: 6:   7 Trignometric Ratios Unit Circle
  78.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  79.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  80.    wt: 6:   3 Trigonometric Ratios sine and cosine
  81.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  82.    wt: 6:   1 Angle Measurement with Degrees
  83.    wt: 6:   8 Distance Between Points on a Line
  84.    wt: 6:   5 Cartesian Addition and Translation
  85.    wt: 6:   PS G Rotation Distributes over Addition
  86.    wt: 6:   PS F Scalar Multiplication Distributes over Addition
  87.    wt: 6:   PS D Addition with Cartesian Coordinates
  88.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  89.    wt: 5:   16 cotangent function Definition Graph and Inverse
  90.    wt: 5:   15 cosecant function Definition Graph and Inverse
  91.    wt: 5:   14 secant function Definition Graph and Inverse
  92.    wt: 5:   13 cosecant function Definition Graph and Inverse
  93.    wt: 5:   12 motivation for term arctan
  94.    wt: 5:   11 arctan left inverse of tangent Graph
  95.    wt: 5:   10 arctan left inverse of tangent Definition
  96.    wt: 5:   9 motivation for name arcsin
  97.    wt: 5:   8 arcsin left inverse of sine Graph
  98.    wt: 5:   7 arcsin left inverse of sine Definition
  99.    wt: 5:   6 Graph of arccos function
  100.    wt: 5:   5 Swapping Coordinates is a reflection
  101.    wt: 5:   4 possible motivation for term arccos
  102.    wt: 5:   3 Left Inverse of cosine arccos definition
  103.    wt: 5:   2 cosine function more properties
  104.    wt: 5:   1 cosine function properties
  105.    wt: 5:   9 Summary Degrees to Radians and back
  106.    wt: 5:   8 Radian Measures of Common Angles
  107.    wt: 5:   7 Radian Measures in special Triangles
  108.    wt: 5:   6 Radian Measure to Degrees
  109.    wt: 5:   5 Degrees to Radian Measure
  110.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  111.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  112.    wt: 5:   2 Radian Measure Numerical Value of one degree
  113.    wt: 5:   1 Degrees and Radians Introduction
  114.    wt: 5:   4 graphing y=Asin(x c)
  115.    wt: 5:   3 graphing y=f(x c) plus K
  116.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  117.    wt: 5:   1 graphing y=f(x a)
  118.    wt: 5:   Parallel Lines and Parallel Transversals
  119.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  120.    wt: 5:   Triangle Angles Sum To 180 Degrees
  121.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  122.    wt: 5:   Parallel Lines and Interior Angles
  123.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  124.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  125.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  126.    wt: 5:   Straight Lines ASA Intersection Study More
  127.    wt: 5:   Straight Lines ASA Intersection Study
  128.    wt: 5:   Straight Lines Instersection Solving Equations
  129.    wt: 5:   Straight Lines Intersection of
  130.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  131.    wt: 5:   C Straight Lines Slope from Coordinates
  132.    wt: 5:   B Straight Line Slope Scaling Properties More
  133.    wt: 5:   A Straight Line Slope Scaling Properties
  134.    wt: 5:   14 Straight Lines Equations General Case
  135.    wt: 5:   12 Straight Lines Graphing mx plus b
  136.    wt: 5:   11 Straight Lines Graphing y=mx
  137.    wt: 5:   10 Straight Lines through Origin Equations More
  138.    wt: 5:   9 Straight Lines through Origin Equations
  139.    wt: 5:   8 Straight Lines Equation for vertical
  140.    wt: 5:   7 Tangent Function is odd on this domain
  141.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  142.    wt: 5:   5 Tangent Function Graph
  143.    wt: 5:   4 Tangent Function Properties
  144.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  145.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  146.    wt: 5:   1 Straight Lines Slope Concept
  147.    wt: 5:   21 Logarithms Powers and Exponentials
  148.    wt: 5:   20 N th Roots of Complex Numbers
  149.    wt: 5:   19 N th Roots of Unity
  150.    wt: 5:   18 Sixth Roots of Unity
  151.    wt: 5:   17 Cube Roots of unity
  152.    wt: 5:   16 References and Originality Question
  153.    wt: 5:   15 Pythagorean Theorem Converse
  154.    wt: 5:   14 Law of cosines
  155.    wt: 5:   13 Trig Formulas for dot and cross Products
  156.    wt: 5:   12 cis formulas for sine cosines and tangent
  157.    wt: 5:   11 sine and cosine double triple angle formulas
  158.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  159.    wt: 5:   9 The complex number valued trig function cis
  160.    wt: 5:   7 Second Way to Calculate Products
  161.    wt: 5:   6 Field Properties of Complex Number
  162.    wt: 5:   5 An Easy Proof of the Distributive Law
  163.    wt: 5:   4 Multiplication Properties
  164.    wt: 5:   2 Complex Numbers made easier we hope
  165.    wt: 5:   1 Rectangular Polar Coordinates Review
  166.    wt: 5:   Appetizer A Complex Number Applet
  167.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  168.    wt: 5:   12 Triangles Similarity More Problems
  169.    wt: 5:   11 Triangle Similarity Missing Side Problem
  170.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  171.    wt: 5:   9 Similarity of Triangles Usual Criteria
  172.    wt: 5:   8 Similarity of Triangles and Polygons
  173.    wt: 5:   7 Translations Rotations Reflections Dilatations
  174.    wt: 5:   6 Geometric Diagrams in Class
  175.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  176.    wt: 5:   4 Similarity Definition with Coordinate
  177.    wt: 5:   3 Similarity by Design with coordinates
  178.    wt: 5:   2 Similarity By Design
  179.    wt: 5:   1 Early Concept of Like or Similar Shapes
  180.    wt: 5:   Four Simple Exercises
  181.    wt: 5:   12 Links Lessons elsewhere
  182.    wt: 5:   11 A Partial Summary
  183.    wt: 5:   10 Midpoint of [a b] and [b a]
  184.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  185.    wt: 5:   8 Mid Point Formula
  186.    wt: 5:   7 Exercises to test skill and concept mastery
  187.    wt: 5:   6 Intersection of lines by solving linear systems
  188.    wt: 5:   5 Algebraic View of Slopes
  189.    wt: 5:   4 Equations for lines three forms
  190.    wt: 5:   3 Slope product for perpendicular lines
  191.    wt: 5:   2 point slope equation for a line
  192.    wt: 5:   1 Numerical view of lines and their equations
  193.    wt: 5:   What is and is not here
  194.    wt: 5:   13 Pythagorean spatial distance formulas
  195.    wt: 5:   12 Spatial Coordinates
  196.    wt: 5:   11 Triangle Inequality
  197.    wt: 5:   10 Pythagorean plane distance formula
  198.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  199.    wt: 5:   7 Complex Numbers Appetizer
  200.    wt: 5:   6 Polar Multiplication and Rotation
  201.    wt: 5:   4 Polar Coordinates to and from
  202.    wt: 5:   3 Rectangular Coordinates Review
  203.    wt: 5:   2 Cartesian Coordinates with signs
  204.    wt: 5:   1 Cartesian Coordinates sans signs
  205.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  206.    wt: 5:   PS H Distributive Law For Complex Numbers
  207.    wt: 5:   PS E Multiplication with Polar Coordinates
  208.    wt: 5:   PS B Parallelogram Construction Methods
  209.    wt: 5:   PS A Kite Construction Methods
  210.    wt: 5:   21 Parallelograms
  211.    wt: 5:   19 Right Triangle Similarity
  212.    wt: 5:   18 Triangle Similarity Take 1
  213.    wt: 5:   17 Right Bisectors of Triangle Sides
  214.    wt: 5:   16 Angles Subtended By Chords and Diameters
  215.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  216.    wt: 5:   14 Parallel Lines Postulate
  217.    wt: 5:   13 Angle Side Angle Failure
  218.    wt: 5:   12 Side Angle Side Failure
  219.    wt: 5:   11 Triangle Construction Fails
  220.    wt: 5:   10 Dropping a perpendicular to line
  221.    wt: 5:   9 Construction of a right bisector
  222.    wt: 5:   8 Isoceles Triangles
  223.    wt: 5:   7 Angle Side Angle
  224.    wt: 5:   6 Ruler and compass Angle Bisection
  225.    wt: 5:   5 Side Angle Side
  226.    wt: 5:   4 Side Side Side
  227.    wt: 5:   3 Isometry of Triangles Congruence
  228.    wt: 5:   2 Correspondence between Triangles
  229.    wt: 5:   1 Initial Concepts and Terms
  230.    wt: 5:   Short Course on Euclidean Geometry
  231.    wt: 5:   About Folder Contents
  232.    wt: 2:   Maps Plans Drawings
  233.    wt: 2:   13 Addition and Addition Tables
  234.    wt: 2:   11 Signed Number Addition and Addition Properties
  235.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  236.    wt: 1:   About site lesson plans
  237.    wt: 1:   3 Polynomials Multiplication Addition
  238.    wt: 1:   21 Addition of Multiples of a Single Vector
  239.    wt: 1:   19 Signed Multiples of Vectors
  240.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  241.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  242.    wt: 1:   15 Head to Tails in place Addition Associative
  243.    wt: 1:   13 Arrows and Vectors in a Plane
  244.    wt: 1:   4 Location of Point in Decimal Addition
  245.    wt: 1:   A Decimal Addition Columm Methods
  246.    wt: 1:   2 Combing Counts Addition Skills and Principles
  247.    wt: 1:   2 Addition and Multiplication Axioms
  248.    wt: 1:   11 Real Number Addition
  249.    wt: 1:   8 Coordinates for Maps and Planes
  250.    wt: 1:   3 GE III Equation Addition and Multiplication
  251.    wt: 1:   3 signed coordinates for maps and planes
  252.    wt: 1:   1 Addition and Subtraction with Units
  253.    wt: 1:   16 Addition Subtraction Comparision Compared
  254.    wt: 1:   1. Explaining Addition Table
  255.    wt: 1:   010 Repeated Addition of Time Intervals
  256.    wt: 1:   8 Addition of Time Intervals via subtotaling
  257.    wt: 1:   7 Addition of Time Intervals
  258.    wt: 1:   Chapter 23 Links To Trigonometry
  259.    wt: 1:   Chapter 21 Arrow Addition
  260.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  261.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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